Kinetic Theory of Plastic Flow in Soft Glassy Materials

A kinetic model for the elastoplastic dynamics of a jammed material is proposed, which takes the form of a nonlocal-Boltzmann-like-kinetic equation for the stress distribution function. Coarse graining this equation yields a nonlocal constitutive law for the flow, exhibiting as a key dynamic quantity the local rate of plastic events. This quantity, interpreted as a local fluidity, is spatially correlated with a correlation length diverging in the quasistatic limit, i.e., close to yielding. In line with recent experimental and numerical observations, we predict finite size effects in the flow behavior, as well as the absence of an intrinsic local flow curve.